Two radioactive elements A and B initially have same number of atoms. half life of A is same as aver

English

Gujarati

Hindi

13.Nuclei

easy

Two radioactive elements $A$ and $B$ initially have same number of atoms. The half life of $A$ is same as the average life of $B$. If $\lambda_A$ and $\lambda_B$ are decay constants of $A$ and $B$ respectively, then choose the correct relation from the given options.

A

$\lambda_{ A }=\lambda_{ B }$

B

$\lambda_{ A }=2 \lambda_{ B }$

C

$\lambda_{ A }=\lambda_{ B } \ln 2$

D

$\lambda_{ A } \ln 2=\lambda_{ B }$

(JEE MAIN-2023)

Solution

$T_{1 / 2}(A)=T_{w N}(B)$

$\frac{\ln 2}{\lambda_{ A }}=\frac{1}{\lambda_{ B }}$

$\lambda_{ A }=\lambda_{ B } \ell 2$

Standard 12

Physics

Share

Similar Questions

Sometimes a radioactive nucleus decays into a nucleus which itself is radioactive. An example is

$\mathop {^{38}S}\limits_{sulpher} \xrightarrow[{ – 2.48\,h}]{{half\,year}}\mathop {^{38}Cl}\limits_{chloride} \xrightarrow[{ – 0.62\,h}]{{half\,year}}\mathop {^{38}Ar}\limits_{Argon} $

Assume that we start with $1000$ $^{38}S$ nuclei at time $t = 0$. The number of $^{38} Cl$ is of count zero at $ t=0$ an will again be zero at $t = \infty $. At what value of $t,$ would the number of counts be a maximum ?

medium

A sample contains $16\, gm$ of a radioactive material, the half life of which is two days. After $32\, days,$ the amount of radioactive material left in the sample is

medium

A radioactive element $ThA (_{84}Po^{216})$ can undergo $\alpha$ and $\beta$ are type of disintegrations with half-lives, $T_1$ and $T_2$ respectively. Then the half-life of ThA is

medium

A radio isotope has a half life of $75\, years$. The fraction of the atoms of this material that would decay in $150\, years$ will be………..$\%$

medium

After five half lives what will be the fraction of initial substance

easy